Jeremy Davis's picture

But in practice I strongly suspect that it would be more trouble than it's worth...

Personally I would start by working out what version of WordPress your current server has and do some googling on how to back up/export the data. Then once you have it safely backed up, google migrating that data to a new server and/or upgrading to a newer version of WordPress. Ideally leave your old server as is as long as possible as then worst case scenario you can go back to that and re export if need be...